Random Gaussian cubic surface Seed: 291 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.126 x*z^2 -0.395 y*z^2 +0.405 z^2 -0.25 x^2*z -0.0767 x*y*z +0.179 x*z +0.312 y^2*z +0.159 y*z -0.137 z +0.201 x^3 -0.24 x^2*y -0.00959 x^2 +0.00867 x*y^2 +0.327 x*y +0.0329 x -0.103 y^3 -0.206 y^2 -0.143 y +0.378 1
Affine cubic: f(x,y,z) = -0.126 x*z^2 -0.395 y*z^2 +0.405 z^2 -0.25 x^2*z -0.0767 x*y*z +0.179 x*z +0.312 y^2*z +0.159 y*z -0.137 z +0.201 x^3 -0.24 x^2*y -0.00959 x^2 +0.00867 x*y^2 +0.327 x*y +0.0329 x -0.103 y^3 -0.206 y^2 -0.143 y +0.378 1
Shadow: the quartic B(x,y)^2 - 4 A(x,y) C(x,y) = 0 is drawn on the z=-4 xy-plane in the same 3D scene. The translucent ruled curtain rises upward from the shadow to the ramification curve where the lifted point has z >= -2 and lies above the displayed projection plane. The 3 real projected lines on the xy-plane are bitangents found from the projective lines on the cubic surface. Same-color transparent line projection cones are included but hidden by default; use the page toggle to show them.
Viewing box: axis ranges are [-4, 4].